WASHINGTON — Facing an unstable economy and an unfinished war, President Bush used his final State of the Union address Monday night to call for quick passage of his tax rebate package, patience in Iraq and a modest concluding agenda that includes $300 million in scholarship money for low-income children in struggling schools.

With Senate Democrats already jockeying to amend the stimulus package that the administration negotiated with the House last week, Bush, in his address, urged lawmakers not to let the delicate deal fall apart.

Like presidents before him, Bush made the case that the state of the union was strong, but he was also forced to concede that Americans felt unsettled about the future.

"As we meet tonight, our economy is undergoing a period of uncertainty," Bush said, adding that "at kitchen tables across the country, there is concern about our economic future."

On Iraq, Bush made the case that his troop buildup had "achieved results few of us could have imagined just one year ago." Yet the president warned that the road ahead would be difficult. "Our enemies in Iraq have been hit hard," he said. "They are not yet defeated, and we can still expect tough fighting ahead."

The White House had promised that the speech would look forward, not back. Yet it was infused with a sense of summing up, as Bush opened by remarking that "our country has been tested in ways none of us could imagine" since he delivered his first address to Congress, seven years ago.

"We have faced hard decisions about peace and war, rising competition in the world economy, and the health and welfare of our citizens," Bush said. "These issues call for vigorous debate, and I think it's fair to say we've answered that call. Yet history will record that amid our differences, we acted with purpose."

Democrats responded to the speech with a call for unity — a departure from past State of the Union evenings, when they have sharply criticized Bush. Gov. Kathleen Sebelius of Kansas, in the Democrats' response on Monday night, urged the president to build on the bipartisanship of the stimulus package — a sign that with the fall elections just 10 months away, Democrats are aware they must show voters they can work across the aisle.

"There is a chance, Mr. President, in the next 357 days, to get real results and give the American people renewed optimism that their challenges are the top priority," Sebelius said. "Working together, working hard, committing to results, we can get the job done."